Question 179281: A rectangular tract of land 20m by 30m has part of its area covered by an I-shaped road, which goes around two sides. The road is the same width on both sides, and its area is 184 square meters. What are the dimensions of the part of the tract of land not covered by the road?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangular tract of land 20m by 30m has part of its area covered by an I-shaped road, which goes around two sides. The road is the same width on both sides, and its area is 184 square meters. What are the dimensions of the part of the tract of land not covered by the road?
:
What's an "I" shaped road? Perhaps you meant an "L" shaped road, assuming that:
:
Find the area of the land not part of the road:
(20*60) - 184 = 416
:
Let = x width of the road
:
Overall area - road area = land tract area
600 - 184 = 416 sq/m
:
write an area equation of the land area not covered by road
(20-x) * (30-x) = 416
FOIL
600 - 20x - 30x + x^2 = 416
x^2 - 50x + 600 - 416 = 0
x^2 - 50x + 184 = 0
Factor
(x-4)(x-46) = 0
Two solutions
x = 46, an impossible answer
and
x = 4 meters is the width of the road
;
Road width subtracted from the overall dimensions to find the dimensions
of the land tract not covered by road
20 - 4 = 16 m
and
30 - 4 = 26 m
:
:
Check solution: 16 * 26 = 416 sq/meters, the area of the land tract
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